First, to construct the score statistic, one needs to plug in some estimate of the nuisance parameter \(\)  such as \(\widehat{}\)  obtained by partitioning \(\widehat{} = (\widehat{\theta },\widehat{}^T)^T\)  in (REF ). However, since \(\)  is a high-dimensional parameter, the estimation error from \(\widehat{}\)  may become the leading term in the asymptotic analysis of the score function.
To deal with the high-dimensional nuisance parameter, we use the decorrelated score, where the key idea is to project the score of the parameter of interest to a high-dimensional nuisance space [1]}.
On the population level, it takes the form
\(\begin{aligned}[b]\nabla _\theta R(\theta ,)-^{*T}\nabla _{} R(\theta ,),\end{aligned}\) 
